We believe that the principles revealed in this work exhaust the many ways one can engineer the phason spaces. They show that, in principle, there is not limit on how high in the virtual dimensions one can go. However, in practice, we expect that the actual laboratory designs to become increasingly challenging and the quality of the topological gaps to wear off as higher virtual dimensions are being conquered. Of course, the next in line is the 6D IQHE, which can be accessed with linear, planar or 3-dimensional meta-material structures. The latter will require a straightforward generalization of the algorithms used in the present work. Let us recall that the bulk-boundary correspondence principle was worked out in arbitrary dimension in [1]} where one can find explicitly solved models as well as an explanation of quantized physical responses.
